The length of a metal wire is $L$, when it is subjected to tension $T$. If the tension is increased to $T+\Delta T$, the length becomes $L+\Delta L$. The natural length of the wire is

If the interatomic spacing in a steel wire is $3.0 \mathring{A}$ and $Y_{\text{steel}} = 20 \times 10^{10} \text{ N/m}^2$, then the force constant is:

Let a steel bar of length $l$,breadth $b$,and depth $d$ be loaded at the centre by a load $W$. Then the sag of bending of the beam is ($Y =$ Young's modulus of the material of steel).

There is some change in length when a $33000 \,N$ tensile force is applied on a steel rod of area of cross-section $10^{-3} \,m^2$. The change of temperature required to produce the same elongation, if the steel rod is heated, is (The modulus of elasticity is $3 \times 10^{11} \,N/m^2$ and the coefficient of linear expansion of steel is $1.1 \times 10^{-5} /{ }^{\circ}C$). (in $^{\circ}C$)

$A$ force is applied to a steel wire '$A$',rigidly clamped at one end. As a result,the elongation in the wire is $0.2\,mm$. If the same force is applied to another steel wire '$B$' of double the length and a diameter $2.4$ times that of the wire '$A$',the elongation in the wire '$B$' will be $............\times 10^{-2}\,mm$ (wires having uniform circular cross sections).

$A$ wire of cross-sectional area $A$,modulus of elasticity $2 \times 10^{11} \text{ N m}^{-2}$,and length $2L = 2 \text{ m}$ is stretched between two vertical rigid supports. When a mass of $2 \text{ kg}$ is suspended at the middle,it sags from its original position,making an angle $\theta = \frac{1}{100} \text{ radian}$ with the horizontal at the points of support. The value of $A$ is . . . . . . $\times 10^{-4} \text{ m}^2$. (Given: $g = 10 \text{ m/s}^2$)